Manitoba
12. Demonstrate understanding of characteristics of quadratic functions
12.2 Transformations of quadratic functions
Chapter 12.2
Transformations of quadratic functions
What You'll Learn
Identify how coefficients and constants transform the parent function y = x²
Apply reflection transformations across the x-axis using negative coefficients
Perform vertical stretches and compressions by multiplying y-values
Execute horizontal and vertical translations by modifying x and y terms
Determine the vertex of a transformed parabola from its equation
Combine multiple transformations to graph complex quadratic functions
What You'll Practice
1
Graphing reflections of parabolas across the x-axis
2
Applying vertical expansions and compressions to quadratic graphs
3
Translating parabolas horizontally and vertically using shifts
4
Combining multiple transformations in a single equation
5
Finding vertex coordinates from transformed quadratic equations
Why This Matters
Transforming quadratic functions is essential for modeling real-world phenomena like projectile motion, profit optimization, and engineering designs. Mastering these transformations gives you the power to quickly sketch and analyze parabolas without plotting dozens of points, a skill you'll use throughout algebra, precalculus, and calculus.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Skills
Quadratic Functions
Transformations
Vertex Form
Reflections
Translations
Vertical Stretch
Horizontal Shift
Graphing Parabolas
MB Curriculum Aligned
